Chapter 3 Modeling of Particle Size Distribution at the Exhaust of Internal Combustion Engines Nowadays, the interest in the effect of exhaust emissions from road vehicles on public health is stronger than ever. Great attention is paid to particulate matter (PM) both for its impact on the environment and for the adverse effect on human health. The internal combustion engines (ICEs), both spark ignition (SI), and compression ignition (CI) are the main sources of PM emissions in the urban area. Particles are usually classified according to their diameter in coarse particles, diameter larger than 10 lm (PM10) and fine particles, diameter smaller than 2.5 lm (PM2.5). Further distinction is made for PM2.5, particles smaller than 100 nm are called ultrafine particles and those smaller than 50 nm are called nanoparticles. The chemical nature of the parti- cles as well as the number and size depends on the engine type. Diesel engine particles consist mainly of agglomerated carbonaceous primary particles on which volatile organic material is adsorbed. The gasoline particles, instead, are mainly composed of organic fraction. Both CI and SI engines emit mainly particles in the ultrafine size range. Anyway, the particles’ emissions from gasoline direct injection (GDI) engines are higher than that for port fuel injection (PFI) engines and Diesel engines equipped with a Diesel particulate filter (DPF). The severe adverse effects on human health of fine and ultrafine particles emitted from internal combustion were well described in the literature [1–3]. Recent studies evidenced the strict relation between the particle size and the impact on heart and brain [4]. Smaller particles can, in fact, penetrate more easily the cell membranes than large particles [5]. Considering the negligible weight of the fine particle, a particle number (PN) emission limit is enforced in addition to the PM mass emission limits for particles larger than 23 nm at the Euro 6 (2014) for all categories of light-duty (LD) DI vehicles. Great efforts are paid to reduce the particle emissions. Several solutions are under study, regarding the optimization of the combustion and the use of biofuel to reduce particle formation as well as the improvement of after-treatment devices for the reduction of emissions at the exhaust. In any case, availability of real-time information on the characteristics of particulate emissions, such as particle number and size, would enable the development of advanced closed-loop control © The Author(s) 2018 F. Taglialatela Scafati et al., Nonlinear Systems and Circuits in Internal Combustion Engines, SpringerBriefs in Nonlinear Circuits, https://doi.org/10.1007/978-3-319-67140-6_3 33